The Generalized Cross Entropy Method, with Applications to Probability Density Estimation

Zdravko I. Botev () and Dirk P. Kroese ()
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Zdravko I. Botev: The University of Queensland
Dirk P. Kroese: The University of Queensland

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 1, 1-27

Abstract: Abstract Nonparametric density estimation aims to determine the sparsest model that explains a given set of empirical data and which uses as few assumptions as possible. Many of the currently existing methods do not provide a sparse solution to the problem and rely on asymptotic approximations. In this paper we describe a framework for density estimation which uses information-theoretic measures of model complexity with the aim of constructing a sparse density estimator that does not rely on large sample approximations. The effectiveness of the approach is demonstrated through an application to some well-known density estimation test cases.

Keywords: Cross entropy; Information theory; Monte Carlo simulation; Statistical modeling; Kernel smoothing; Functional optimization; Bandwidth selection; Calculus of variations; Primary 94A17, 60K35; Secondary 68Q32, 93E14 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s11009-009-9133-7

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